Find the marginal rate of substitution given the following utility functions for X and y: U(x) = 2xy U(y) = 3x1/3,2/3 O x1/3 / yA/3 2/3 x2/3y1/3 O y2/3 / x1/3 O yA13 / x1/3
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- Find the marginal rate of substitution given the following utility functions for x and y: U(x) = 2xy U(y) = 3x1/3,2/3 O x1/3 / yA/3 O 213 x213y1/3 y2/3 / x1/3 'yA/3 /x1/3It is common for supermarkets to carry both generic (store-label) and brand-name (producer-label) varieties of sugar and other products. Many consumers view these products as perfect substitutes, meaning that consumers are always willing to substitute a constant proportion of the store brand for the producer brand. Consider a consumer who is always willing to substitute 4 pounds of a generic store brand for 2 pounds of a brand-name sugar. Do these preferences exhibit a diminishing marginal rate of substitution? Assume that this consumer has $24 of income to spend on sugar, and the price of store-brand sugar is $1 per pound and the price of producer-brand sugar is $3 per pound. How much of each type of sugar will be purchased? How would your answer change if the price of store-brand sugar was $2 per pound and the price of producer-brand sugar was $3 per pound?Define the Marginal Rate of Substitution between two goods (X and Y).If a consumer’s preferences are given by U(X,Y) = X1/4Y 3/4, compute the consumer’s marginalrate of substitution as a function of X and Y. Calculate the MRS if the consumer has chosen toconsumer 12 units of X and 30 units of Y.
- 1 Marginal utility and marginal rate of substitution Suppose an individual who derives utility u(x, y) from consuming a units of good X and y units of good Y. For each of the following utility functions, derive the marginal utility of good X, the marginal utility of good Y, and the marginal rate of substitution between X and Y. (A) u(x, y) = x+by¹/3 (B) u(x, y) = (xy) (C) u(x, y) = ax + xy + by² (D) u(x, y) = n(ax + y) 1 (E) u(x, y) = (x² + √y²) = 2Calculate the marginal rate of substitution (MRS12) for the following utility function: U(91, 92) (1491 +692)³. What is the value of MRS12 at bundle (4, 8)? Please round your answer to two decimal places if necessary.1. For each of the three utility functions below, find the substitution effect, the income effect, and the total effect that result when prices change from p = (2,1) to p' = (2,4). Assume the consumer has income I = 20. (a) Before doing any calculation, make an educated guess about the relative magnitude of the three substitution effects and the three income effects to be found below. (b) u(x1, x2) = x1 + x2. (c) u(x1, x2) = x1x2. (d) u(x1,x2) = min {x1,x2). (e) Rank the substitution effects and the income effects found above by their magnitude. To what extent do they conform to your guess?
- Find the marginal utility (MU) and marginal rate of substitution (MRS) of following utility functions. 1. U(x1,x2)=ln(x1)+x2,findMUx1,MUx2,andMRS(x1,x2) 2. U(x1,x2)=(2x21+x32)1/2,findMUx1,MUx2,andMRS(x1,x2)Number of Sodas per day Total Utility Marginal Utilit 1 20 35 3 47 12 4 10 Refer to the table, The marginal utility of the second soda per day is L. (Answer should be in the form of numerical characters, e.g. 20) Enter your answer hereASAP 1. Consider a consumer with utility u(x1,x2) = .5lnx1 + .5lnx2 (b) Now, consider an equivalent representation of the above utility functionx51 x52 Does this utility function have the "increasing difference property"? Howabout the "strict increasing difference" property?
- Consider the following utility function. U=U(X,Y)=X0.2Y0.8 Find the marginal utilities. Determine their signs. Provide the economic interpretation of the signs of these marginal utilities. Determine whether the law of diminishing marginal utility holds for both goods.QUESTION 1 Let qa be the quantity of apples and qo the quantity of oranges. A consumer's utility is described by the function u(qA.90)= 39A + 590 This consumer curently consumes 2 apples and 4 oranges. For this consumer, the marginal utilities are MUA= and MUO= Moreover, the marginal rate of substitution is MRSA O=For the utility function U(X,Y)= 6X0.50.5, the marginal rate of substitution MRSxy is: O Y/X. O X/Y. 3Y/X. O3X/Y.